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  $H_2O$ $CO_2$ $C_2H_6$ $\frac{ 1 }{ 2 }$ $\displaystyle \frac{ 1 }{ 2 }$ $\left( - \frac{ 1 }{ 2 } \right )^2$ $\frac{ a + b }{ c + \frac{ d }{ e } }$ $\begin{eqnarray}1 + \frac{ 1 }{ 1 + \frac{ 1 }{ 1 + \frac{ 1 }{ 1 + \ddots } } }= \frac{ 1 }{ 2 } \left( 1 + \sqrt{ 5 } \right)\end{eqnarray}$ $0.123$ $\frac{ 1 }{ 11 } = 0.\dot{ 0 } \dot{ 9 }$ $3.14 \ldots$ $\sqrt{ 2 } = 1.4142 \ldots$ $\infty$ $| x |$ $\vert x \vert$ $\left| \frac{ x }{ 2 } \right|$ $[ x ]$ $\lbrack x \rbrack$ $\lfloor x \rfloor$ $\lceil x \rceil$ $1 + 2$ $3 - 1$ $2 \times 3$ $6 \div 3$ $\pm 1$ $\mp 1$ $a \cdot b = ab$ $a / b = \frac{a}{b}$ $a \equiv b \bmod n$ $a \equiv b \pmod n$ $x \propto y$ $a \gt b$ $a \geqq b$ $a \lt b$ $a \leqq b$ $a = b$ $a \neq b$ $a \fallingdotseq b$ $a \sim b$ $a \simeq b$ $a \approx b$ $a \gg b$ $a \ll b$ $\max f(x)$ $\min f(x)$ $x \in A$ $A \ni x$ $x \notin A$ $A \subset B$ $A \subseteq B$ $A \subseteqq B$ $A \supset B$ $A \supseteq B$ $A \supseteqq B$ $A \not \subset B$ $A \subsetneqq B$ $A \cap B$ $A \cup B$ $\varnothing$ $A^c$ $\overline{ A }$ $A \setminus B$ $A \setminus B = A \cap B^c = \{ x \mid x \in A, x \notin B \}$ $\mathbb{ N }$ $\mathbb{ Z }$ $\mathbb{ Q }$ $\mathbb{ R }$ $\mathbb{ C }$ $\mathbb{ H }$ $\sup A$ $\inf A$ $\aleph$ $P \land Q$ $P \lor Q$ $\lnot P$ $\overline{ P }$ $!P$ $P \Rightarrow Q$ $P \to Q$ $P \implies Q$ $P \Leftarrow Q$ $P \gets Q$ $P \Leftrightarrow Q$ $P \leftrightarrow Q$ $P \iff Q$ $P \equiv Q$ $P \models Q$ $\forall x$ $\exists x$ $\nexists$ $\therefore$ $\because$ ${}_n \mathrm{ P }_k$ ${}_n \mathrm{ C }_k$ $n!$ $\binom{ n }{ k }$ ${ n \choose k }$ ${}_n \prod_k$ ${}_n \mathrm{ H }_k$ $\begin{eqnarray}{}_n \mathrm{ P }_k = n \cdot ( n - 1 ) \cdots ( n - k + 1 ) = \frac{ n! }{ ( n - k )! }\end{eqnarray}$ $\begin{eqnarray}{}_n \mathrm{ C }_k = \binom{ n }{ k } = \frac{ n! }{ k! ( n - k )! }\end{eqnarray}$ $\sum_{ i = 1 }^{ n } a_n$ $\displaystyle \sum_{ i = 1 }^{ n } a_n$ $\begin{eqnarray}\sum_{ k = 1 }^{ n } k^2 = \overbrace{ 1^2 + 2^2 + \cdots + n^2 }^{ n } = \frac{ 1 }{ 6 } n ( n + 1 ) ( 2n + 1 )\end{eqnarray}$ $\prod_{ i = 0 }^n x_i$ $\displaystyle \prod_{ i = 0 }^n x_i$ $\begin{eqnarray}n! = \prod_{ k = 1 }^n k\end{eqnarray}$ $\begin{eqnarray}\zeta (s) = \prod_{ p:\mathrm{ prime } } \frac{ 1 }{ 1 - p^{ -s } }\end{eqnarray}$ $2^3$ $e^{ i \pi }$ $\exp ( x )$ $\sqrt{ 2 }$ $\sqrt{ \mathstrut a } + \sqrt{ \mathstrut b }$ $\sqrt[ n ]{ x }$ $\log x$ $\log_{ 2 } x$ $\ln x$ $90^{ \circ }$ $\frac{ \pi }{ 2 }$ $\angle A$ $AB /\!/ CD$ $AB \parallel CD$ $AB \perp CD$ $\triangle ABC$ $\Box ABCD$ $\stackrel{ \Large \frown }{ AB }$ $\triangle ABC \equiv \triangle DEF$ $\triangle ABC \backsim \triangle DEF$ $\triangle ABC \sim \triangle DEF$ $\sin x$ $\cos x$ $\tan x$ $\begin{eqnarray}\sin 45^\circ = \frac{ \sqrt{2} }{ 2 }\end{eqnarray}$ $\begin{eqnarray}\cos \frac{ \pi }{ 3 } = \frac{ 1 }{ 2 }\end{eqnarray}$ $\begin{eqnarray}\tan \theta = \frac{ \sin \theta }{ \cos \theta }\end{eqnarray}$ $\sec x$ $\csc x$ $\cot x$ $\arcsin x$ $\arccos x$ $\arctan x$ $\sinh x$ $\cosh x$ $\tanh x$ $\coth x$ $\lim_{ x \to +0 } \frac{ 1 }{ x } = \infty$ $\displaystyle \lim_{ n \to \infty } f_n(x) = f(x)$ $\limsup_{ n \to \infty } a_n$ $\varlimsup_{ n \to \infty } a_n$ $\liminf_{ n \to \infty } a_n$ $\varliminf_{ n \to \infty } a_n$ $\begin{eqnarray}\varlimsup_{ n \to \infty } a_n = \lim_{ n \to \infty } \sup_{ k \geqq n } a_k\end{eqnarray}$ $\begin{eqnarray}\varliminf_{ n \to \infty } A_n = \bigcup_{ n = 1 }^{ \infty } \bigcap_{ k = n }^{ \infty } A_k = \bigcup_{ n \in \mathbb{ N } } \bigcap_{ k \geqq n } A_k\end{eqnarray}$ $\frac{ dy }{ dx }$ $\frac{ \mathrm{ d } y }{ \mathrm{ d } x }$ $\frac{ d^n y }{ dx^n }$ $\left. \frac{ dy }{ dx } \right|_{ x = a }$ $f'$ $f^{ ( n ) }$ $Df$ $D_x f$ $D^n f$ $\dot{ y } = \frac{ dy }{ dt }$ $\ddddot{ y } = \frac{ d^4 y }{ dt^4 }$ $\begin{eqnarray}f'(x) = \frac{ df }{ dx } = \lim_{ \Delta x \to 0 } \frac{ f(x + \Delta x) - f(x) }{ \Delta x }\end{eqnarray}$ $\frac{ \partial f }{ \partial x }$ $\frac{ \partial }{ \partial y } \frac{ \partial }{ \partial x } z$ $f_x$ $f_{ xy }$ $\nabla f$ $\Delta f$ $\begin{eqnarray}\Delta \varphi = \nabla^2 \varphi = \frac{ \partial^2 \varphi }{ \partial x^2 } + \frac{ \partial^2 \varphi }{ \partial y^2 } + \frac{ \partial^2 \varphi }{ \partial z^2 }\end{eqnarray}$ $\int_0^1 f(x) dx$ $\displaystyle \int_{ - \infty }^{ \infty } f(x) dx$ $\begin{eqnarray}\int_0^1 x dx = \left[ \frac{ x^2 }{ 2 } \right]_0^1 = \frac{ 1 }{ 2 }\end{eqnarray}$ $\iint_D f(x,y) dxdy$ $\iiiint_D f dxdydzdw$ $\idotsint_D f(x_1, x_2, \ldots , x_n) dx_1 \cdots dx_n$ $\oint_C f(z) dz$ $\vec{ a }$ $\overrightarrow{ AB }$ $\boldsymbol{ A }$ $( a_1, a_2, \ldots, a_n )$ $\boldsymbol{ \rm{ e } }_k = ( 0, \ldots, 0, \stackrel{ k }{ 1 }, 0, \ldots, 0 )^{ \mathrm{ T } }$ $\| x \|$ $\vec{ a } \cdot \vec{ b }$ $\vec{ a } \times \vec{ b }$ $A^{ \mathrm{ T } }$ ${}^t \! A$ $\dim$ $\mathrm{ rank } A$ $\mathrm{ Tr } A$ $\mathrm{ det }A$ $| x |$ $\vert x \vert$ $\{ x \mid x \in A \}$ $\Vert x \Vert$ $AB \parallel CD$ $\overline{ A }$ $\bar{ A }$ $\underline{ A }$ $/$ $\backslash$ $\leftarrow$ $\longleftarrow$ $\rightarrow$ $\longrightarrow$ $\uparrow$ $\downarrow$ $\leftrightarrow$ $\longleftrightarrow$ $\updownarrow$ $\Leftarrow$ $\Longleftarrow$ $\Rightarrow$ $\Longrightarrow$ $\Uparrow$ $\Downarrow$ $\Leftrightarrow$ $\Longleftrightarrow$ $\Updownarrow$ $\mapsto$ $\longmapsto$ $\nearrow$ $\searrow$ $\nwarrow$ $\swarrow$ $\vec{ a }$ $\overrightarrow{ AB }$ $\overleftarrow{ AB }$ $( x )$ $[ x ]$ $\lbrack x \rbrack$ $\lceil x \rfloor$ $\lfloor x \rceil$ $\{ x \}$ $\lbrace x \rbrace$ $\langle x \rangle$ $\left[ \frac{ 1 }{ 2 } \right]$ $\overbrace{ x + y + z }$ $\overbrace{ a_1 + \cdots + a_n }^{ n }$ $\underbrace{ x + y + z }$ $\underbrace{ a_1 + \cdots + a_n }_{ n }$ $\cdot$ $\cdots$ $\ldots$ $\vdots$ $\ddots$ $\dot{ a }$ $\ddot{ a }$ $\circ$ $\bullet$ $\bigcirc$ $\oplus$ $\ominus$ $\otimes$ $\odot$ $\triangle$ $\bigtriangleup$ $\bigtriangledown$ $\triangleleft$ $\lhd$ $\triangleright$ $\rhd$ $\unlhd$ $\unrhd$ $\ast$ $\star$ $\ltimes$ $\rtimes$ $\diamondsuit$ $\heartsuit$ $\clubsuit$ $\spadesuit$ $\flat$ $\natural$ $\sharp$ $\dagger$ $\ddagger$ $aaa \ bbb$ $aaa \quad bbb$ $aaa \qquad bbb$ $aaa \hspace{ 10pt } bbb$ $aaa \! bbb$ $\tiny{ abc ABC }$ $\scriptsize{ abc ABC }$ $\small{ abc ABC }$ $\normalsize{ abc ABC }$ $\large{ abc ABC }$ $\Large{ abc ABC }$ $\LARGE{ abc ABC }$ $\huge{ abc ABC }$ $\Huge{ abc ABC }$ $\mathrm{ ABCDEFGHIJKLMNOPQRSTUVWXYZ \ abcdefghijklmnopqrstuvwxyz }$ $\mathtt{ ABCDEFGHIJKLMNOPQRSTUVWXYZ \ abcdefghijklmnopqrstuvwxyz }$ $\mathsf{ ABCDEFGHIJKLMNOPQRSTUVWXYZ \ abcdefghijklmnopqrstuvwxyz }$ $\mathcal{ ABCDEFGHIJKLMNOPQRSTUVWXYZ }$ $\mathbf{ ABCDEFGHIJKLMNOPQRSTUVWXYZ \ abcdefghijklmnopqrstuvwxyz }$ $\mathit{ ABCDEFGHIJKLMNOPQRSTUVWXYZ \ abcdefghijklmnopqrstuvwxyz }$ $\mathbb{ ABCDEFGHIJKLMNOPQRSTUVWXYZ }$ $\mathscr{ ABCDEFGHIJKLMN \ OPQRSTUVWXYZ }$ $\mathfrak{ ABCDEFGHIJKLMNOPQRSTUVWXYZ \ abcdefghijklmnopqrstuvwxyz }$ $a^{ xy }$ ${}^{ xy } a$ $a_{ xy }$ ${}_{ xy } a$ $\begin{eqnarray}a_n^2 + a_{ n + 1 }^2 = a_{ 2n + 1 }\end{eqnarray}$ $\hat{ a }$ $\grave{ a }$ $\acute{ a }$ $\dot{ a }$ $\ddot{ a }$ $\bar{ a }$ $\vec{ a }$ $\check{ a }$ $\tilde{ a }$ $\breve{ a }$ $\widehat{ AAA }$ $\widetilde{ AAA }$ $\alpha$ $\beta$ $\gamma$ $\delta$ $\epsilon$ $\varepsilon$ $\zeta$ $\eta$ $\theta$ $\vartheta$ $\iota$ $\kappa$ $\lambda$ $\mu$ $\nu$ $\xi$ $o$ $\pi$ $\varpi$ $\rho$ $\varrho$ $\sigma$ $\varsigma$ $\tau$ $\upsilon$ $\phi$ $\varphi$ $\chi$ $\psi$ $\omega$ $A$ $B$ $\Gamma$ $\varGamma$ $\Delta$ $\varDelta$ $E$ $Z$ $H$ $\Theta$ $\varTheta$ $I$ $K$ $\Lambda$ $\varLambda$ $M$ $N$ $\Xi$ $\varXi$ $O$ $\Pi$ $\varPi$ $P$ $\Sigma$ $\varSigma$ $T$ $\Upsilon$ $\varUpsilon$ $\Phi$ $\varPhi$ $X$ $\Psi$ $\varPsi$ $\Omega$ $\varOmega$ $\S$ $\TeX$ $\LaTeX$ $10^{1024}$ $E=mc^2$ $e^{i\theta}=\cos\theta+i\sin\theta$ $i\hbar\frac{\partial\psi}{\partial t} = -\frac{\hbar^2}{2m}\frac{\partial^2\psi}{\partial x^2}+V(x,t)\psi$ $\frac{\partial^2 z}{\partial t^2}=c^2 (\frac{\partial^2 z}{\partial x^2}+\frac{\partial^2 z}{\partial y^2})-\mu \frac{\partial z}{\partial t}$ $G_{\mu\nu}+\Lambda g_{\mu\nu}=\frac{8\pi G}{c^4}T_{\mu\nu}$